Stationary absolute distributions for chains of infinite order

Let {Ƶ_n}^∞_{n = -∞} be a stochastic process with state space S₁ = {0, 1, …, D – 1}. Such a process is called a chain of infinite order. The transitions of the chain are described by the functions

Q_i(i⁽⁰⁾) = Ƥ(Ƶ_n = i | Ƶ_{n - 1} = i ⁽⁰⁾₁, Ƶ_{n - 2} = i ⁽⁰⁾₂, …) (i ɛ S₁), where i⁽⁰⁾ = (i⁽⁰⁾₁, i⁽⁰⁾₂, …) ranges over infinite sequences from S₁. If i⁽ⁿ⁾ = (i⁽ⁿ⁾₁, i⁽ⁿ⁾₂, …) for n = 1, 2,…, then i⁽ⁿ⁾ → i⁽⁰⁾ means that for each k, i⁽ⁿ⁾_k = i⁽⁰⁾_k for all n sufficiently large.

Given functions Q_i(i⁽⁰⁾) such that

(i) 0 ≤ Q_i(i⁽⁰) ≤ ξ ˂ 1

(ii)D – 1/Ʃ/i = 0 Q_i(i⁽⁰⁾) Ξ 1

(iii) Q_i(i⁽ⁿ⁾) → Q_i(i⁽⁰⁾) whenever i⁽ⁿ⁾ → i⁽⁰⁾,

we prove the existence of a stationary chain of infinite order {Ƶ_n} whose transitions are given by

Ƥ (Ƶ_n = i | Ƶ_{n - 1}, Ƶ_{n - 2}, …) = Q_i(Ƶ_{n - 1}, Ƶ_{n - 2}, …)

With probability 1. The method also yields stationary chains {Ƶ_n} for which (iii) does not hold but whose transition probabilities are, in a sense, “locally Markovian.” These and similar results extend a paper by T.E. Harris [Pac. J. Math., 5 (1955), 707-724].

Included is a new proof of the existence and uniqueness of a stationary absolute distribution for an Nth order Markov chain in which all transitions are possible. This proof allows us to achieve our main results without the use of limit theorem techniques.

Stationary Eddies and Zonal Variations of the Global Hydrological Cycle in a Changing Climate

This thesis advances our physical understanding of the sensitivity of the hydrological cycle to global warming. Specifically, it focuses on changes in the longitudinal (zonal) variation of precipitation minus evaporation (P - E), which is predominantly controlled by planetary-scale stationary eddies. By studying idealized general circulation model (GCM) experiments with zonally varying boundary conditions, this thesis examines the mechanisms controlling the strength of stationary-eddy circulations and their role in the hydrological cycle. The overarching goal of this research is to understand the cause of changes in regional P - E with global warming. An understanding of such changes can be useful for impact studies focusing on water availability, ecosystem management, and flood risk.

Based on a moisture-budget analysis of ERA-Interim data, we establish an approximation for zonally anomalous P - E in terms of surface moisture content and stationary-eddy vertical motion in the lower troposphere. Part of the success of this approximation comes from our finding that transient-eddy moisture fluxes partially cancel the effect of stationary-eddy moisture advection, allowing divergent circulations to dominate the moisture budget. The lower-tropospheric vertical motion is related to horizontal motion in stationary eddies by Sverdrup and Ekman balance. These moisture- and vorticity-budget balances also hold in idealized and comprehensive GCM simulations across a range of climates.

By examining climate changes in the idealized and comprehensive GCM simulations, we are able to show the utility of the vertical motion P - E approximation for splitting changes in zonally anomalous P - E into thermodynamic and dynamic components. Shifts in divergent stationary-eddy circulations dominate changes in zonally anomalous P - E. This limits the local utility of the "wet gets wetter, dry gets drier” idea, where existing P - E patterns are amplified with warming by the increase in atmospheric moisture content, with atmospheric circulations held fixed. The increase in atmospheric moisture content manifests instead in an increase in the amplitude of the zonally anomalous hydrological cycle as measured by the zonal variance of P - E. However, dynamic changes, particularly the slowdown of divergent stationary-eddy circulations, limit the strengthening of the zonally anomalous hydrological cycle. In certain idealized cases, dynamic changes are even strong enough to reverse the tendency towards "wet gets wetter, dry gets drier” with warming.

Motivated by the importance of stationary-eddy vertical velocities in the moisture budget analysis, we examine controls on the amplitude of stationary eddies across a wide range of climates in an idealized GCM with simple topographic and ocean-heating zonal asymmetries. An analysis of the thermodynamic equation in the vicinity of topographic forcing reveals the importance of on-slope surface winds, the midlatitude isentropic slope, and latent heating in setting the amplitude of stationary waves. The response of stationary eddies to climate change is determined primarily by the strength of zonal surface winds hitting the mountain. The sensitivity of stationary-eddies to this surface forcing increases with climate change as the slope of midlatitude isentropes decreases. However, latent heating also plays an important role in damping the stationary-eddy response, and this damping becomes stronger with warming as the atmospheric moisture content increases. We find that the response of tropical overturning circulations forced by ocean heat-flux convergence is described by changes in the vertical structure of moist static energy and deep convection. This is used to derive simple scalings for the Walker circulation strength that capture the monotonic decrease with warming found in our idealized simulations.

Through the work of this thesis, the advances made in understanding the amplitude of stationary-waves in a changing climate can be directly applied to better understand and predict changes in the zonally anomalous hydrological cycle.

Theoretical investigations of experimental gravitation

This thesis has two basic themes: the investigation of new experiments which can be used to test relativistic gravity, and the investigation of new technologies and new experimental techniques which can be applied to make gravitational wave astronomy a reality.

Advancing technology will soon make possible a new class of gravitation experiments: pure laboratory experiments with laboratory sources of non-Newtonian gravity and laboratory detectors. The key advance in techno1ogy is the development of resonant sensing systems with very low levels of dissipation. Chapter 1 considers three such systems (torque balances, dielectric monocrystals, and superconducting microwave resonators), and it proposes eight laboratory experiments which use these systems as detectors. For each experiment it describes the dominant sources of noise and the technology required.

The coupled electro-mechanical system consisting of a microwave cavity and its walls can serve as a gravitational radiation detector. A gravitational wave interacts with the walls, and the resulting motion induces transitions from a highly excited cavity mode to a nearly unexcited mode. Chapter 2 describes briefly a formalism for analyzing such a detector, and it proposes a particular design.

The monitoring of a quantum mechanical harmonic oscillator on which a classical force acts is important in a variety of high-precision experiments, such as the attempt to detect gravitational radiation. Chapter 3 reviews the standard techniques for monitoring the oscillator; and it introduces a new technique which, in principle, can determine the details of the force with arbitrary accuracy, despite the quantum properties of the oscillator.

The standard method for monitoring the oscillator is the "amplitude- and-phase" method (position or momentum transducer with output fed through a linear amplifier). The accuracy obtainable by this method is limited by the uncertainty principle. To do better requires a measurement of the type which Braginsky has called "quantum nondemolition." A well-known quantum nondemolition technique is "quantum counting," which can detect an arbitrarily weak force, but which cannot provide good accuracy in determining its precise time-dependence. Chapter 3 considers extensively a new type of quantum nondemolition measurement - a "back-action-evading" measurement of the real part X₁ (or the imaginary part X₂) of the oscillator's complex amplitude. In principle X₁ can be measured arbitrarily quickly and arbitrarily accurately, and a sequence of such measurements can lead to an arbitrarily accurate monitoring of the classical force.

Chapter 3 describes explicit gedanken experiments which demonstrate that X₁ can be measured arbitrarily quickly and arbitrarily accurately, it considers approximate back-action-evading measurements, and it develops a theory of quantum nondemolition measurement for arbitrary quantum mechanical systems.

In Rosen's "bimetric" theory of gravity the (local) speed of gravitational radiation v_g is determined by the combined effects of cosmological boundary values and nearby concentrations of matter. It is possible for v_g to be less than the speed of light. Chapter 4 shows that emission of gravitational radiation prevents particles of nonzero rest mass from exceeding the speed of gravitational radiation. Observations of relativistic particles place limits on v_g and the cosmological boundary values today, and observations of synchrotron radiation from compact radio sources place limits on the cosmological boundary values in the past.

Eutrophication and the management of planktonic algae: What Vollenweider couldn't tell us

The ”Vollenweider model” is a sophisticated mathematical statement about the long-range behaviour of (mainly temperate) lakes and their ability to support phytoplankton chlorophyll. Misapplication of the model, against which Vollenweider himself warned, has led to many misconceptions about the dynamics of plankton in lakes and reservoirs and about how best to manage systems subject to eutrophication. This contribution intends to frame the most important issues in context of the phosphorus- loading and phosphorus-limitation concepts. Emphasis is placed on the need to distinguish rate-limitation from capacity-limitation, to understand which is more manageable and why, to discern the mechanisms of internal recycling and their importance, and to appreciate the respective roles of physical and biotic components in local control of algal dynamics. Some general approaches to the management of water quality in lakes and reservoirs to eutrophication are outlined.

Dynamic response of hysteretic systems with application to a system containing limited slip

A general class of single degree of freedom systems possessing rate-independent hysteresis is defined. The hysteretic behavior in a system belonging to this class is depicted as a sequence of single-valued functions; at any given time, the current function is determined by some set of mathematical rules concerning the entire previous response of the system. Existence and uniqueness of solutions are established and boundedness of solutions is examined.

An asymptotic solution procedure is used to derive an approximation to the response of viscously damped systems with a small hysteretic nonlinearity and trigonometric excitation. Two properties of the hysteresis loops associated with any given system completely determine this approximation to the response: the area enclosed by each loop, and the average of the ascending and descending branches of each loop.

The approximation, supplemented by numerical calculations, is applied to investigate the steady-state response of a system with limited slip. Such features as disconnected response curves and jumps in response exist for a certain range of system parameters for any finite amount of slip.

To further understand the response of this system, solutions of the initial-value problem are examined. The boundedness of solutions is investigated first. Then the relationship between initial conditions and resulting steady-state solution is examined when multiple steady-state solutions exist. Using the approximate analysis and numerical calculations, it is found that significant regions of initial conditions in the initial condition plane lead to the different asymptotically stable steady-state solutions.

Results on proximal and generalized weak proximal contractions including the case of iteration-dependent range sets

This paper presents some further results on proximal and asymptotic proximal contractions and on a class of generalized weak proximal contractions in metric spaces. The generalizations are stated for non-self-mappings of the forms for and , or , subject to and , such that converges uniformly to T, and the distances are iteration-dependent, where , , and are non-empty subsets of X, for , where is a metric space, provided that the set-theoretic limit of the sequences of closed sets and exist as and that the countable infinite unions of the closed sets are closed. The convergence of the sequences in the domain and the image sets of the non-self-mapping, as well as the existence and uniqueness of the best proximity points, are also investigated if the metric space is complete. Two application examples are also given, being concerned, respectively, with the solutions through pseudo-inverses of both compatible and incompatible linear algebraic systems and with the parametrical

Spectroscopic properties of neodymium doped high silica glass and aluminum codoping effects on the enhancement of fluorescence emission

Nd3+ -codoped and Al3+-Nd3+-codoped high silica glasses have been prepared by sintering nanoporous glasses impregnated with Nd3+ stop and Al3+ ions. The Judd-Ofelt intensity parameters Omega(2,4,6) of Nd3+-doped high silica glasses were obtained and used to analyze aluminum codoping effects. Fluorescence properties of Nd3+-doped high silica glasses strongly depend on the Al3+ concentration. While Nd3+ ion absorption and emission intensities of obviously increase when aluminum is added to Nd3+-doped high silica glasses, fluorescence lifetimes decrease and aluminum codoping has almost no influence on the radiative quantum efficiencies. This indicates that aluminum codoping is responsible for an anti-quenching effect through a local modification of rare-earth environments rather than through physical cluster dispersion.

Structural role of fluoride in aluminophosphate sol-gel glasses: High-resolution double-resonance NMR studies

The local structure of Na-Al-P-O-F glasses, prepared by a novel sol-gel route, was extensively investigated by advanced solid-state NMR techniques. Al-21{F-19} rotational echo double resonance (REDOR) results indicate that the F incorporated into aluminophosphate glass is preferentially bonded to octahedral Al units and results in a significant increase in the concentration of six-coordinated aluminum. The extent of Al-F and Al-O-P connectivities are quantified consistently by analyzing Al-27{P-31} and Al-21{F-19} REDOR NMR data. Two distinct types of fluorine species were identified and characterized by various F-19{Al-27}, F-19{Na-23}, and F-19{P-31} double resonance experiments, which were able to support peak assignments to bridging (Al-F-Al, -140 ppm) and terminal (Al-F, -170 ppm) units. On the basis of the detailed quantitative dipole-dipole coupling information obtained, a comprehensive structural model for these glasses is presented, detailing the structural speciation as a function of composition.

A relação entre indústria farmacêutica e a assistência farmacêutica no âmbito do Sistema Único de Saúde (SUS): a compra estadual e municipal de medicamentos no Rio de Janeiro

Esta dissertação tem como objeto o estudo da relação estabelecida entre a indústria farmacêutica e a assistência farmacêutica no âmbito do SUS. O objetivo é avaliar como estão sendo feitas as compras de medicamentos para os programas de assistência farmacêutica básica para hipertensão, diabetes e asma e rinite. A captura de dados foi realizada nas Secretarias de Saúde do estado e do município do Rio de Janeiro. Realizou-se comparação dos preços unitários dos medicamentos adquiridos no estado, no município do Rio de Janeiro e no Banco de Preços em Saúde (BPS), no período de janeiro de 2000 a dezembro de 2006. Em alguns momentos foram utilizados dados da Revista ABCFARMA, sobre preços unitários do mercado varejista. A pesquisa tornou possível registrar que o Estado do Rio de Janeiro compra medicamentos a um preço unitário mais alto do que aqueles praticados pela prefeitura e pelo Banco de Preços em Saúde. A hipótese apresentada é que o preço unitário mais alto se deve às inúmeras compras emergenciais realizadas, que estimulam os fornecedores a compensar o risco com preços maiores. Como a maioria dos fornecedores é distribuidora de medicamentos, elas estariam onerando os preços unitários, pois tiveram problemas no passado com o cumprimento da dívida pelo estado. Segundo autoridades estaduais da Secretaria de Estado de Saúde, esta situação indesejável está sendo superada através de uma nova forma de aquisição de medicamentos. A prefeitura do Rio de Janeiro, por outro lado, tem realizado as compras de medicamentos por licitações na modalidade concorrência. Esta forma possibilitou a aquisição de medicamentos a preços inferiores aos outros entes pesquisados. A maioria dos fornecedores da prefeitura é a própria indústria de medicamentos, o que, em princípio, torna o preço mais baixo. Conclui-se, então: que o Estado do Rio de Janeiro passou por crises de desabastecimento ou abastecimento irregular dos programa de assistência farmacêutica básica, o que contribuiu para a elevação dos preços praticados; e que a prefeitura do Rio de Janeiro tem conseguido comprar medicamentos em condições mais favoráveis que o governo de estado.

Announcing the release of FishBase 96

FishBase is a computerized encyclopedia of fishes developed at International Center for Living Aquatic Resources Management (ICLARM) with the support of the European Commission and in collaboration with a large number of institutions throughout the world, notably FAO, and available since 1995 as CD-ROM. Major improvements since version 1.2 have now allowed for the release of FishBase 96, whose name indicates the intention to update FishBase annually. Some of the major improvements of FishBase 96 are: (a) 3,000 more species (total 15,000) and 3,000 more pictures (total 9,000); (b) complete marine checklists for 48 countries, and freshwater checklists for 60 countries; (c) a new user module to document local knowledge of fishes; (d) a stand-alone glossary defining 2,500 ichthyological and related terms; (e) new databases on brain weights (from R. Beauchot and colleagues at the University of Paris VII), on ciguatera (from P. Dalzell, South Pacific Commission, Noumea), and on recruitment (from R.A. Myers and colleagues at the Department of Fisheries and Oceans, St. John's); and (f) new graphs to display quantitative data: through time series, pie charts and bivariate plots. As before, FishBase is available free to collaborators, for US$50 as update to registered users of previous versions, and for US$95 for new users.

Effect of diazinon 60 EC on Anabas testudineus, Channa punctatus and Barbodes gonionotus

Anabas testudineus, Channa punctatus and Barbodes gonionotus were exposed to 5.62, 6.25, 6.87, 7.50, 8.12 and 8.75 ppm; 1.13, 2.26, 3.39, 4.52, 5.65 and 6.78 ppm; and 2.00, 2.50, 3.00, 3.50, 4.00 and 4.50 ppm of Diazinon 60 EC, respectively. The median lethal concentration (LC50) values of Diazinon 60 EC on A. testudineus, C. punctatus and B. gonionotus were 6.55, 3.09 and 2.72 ppm for 96 hrs of exposure. The fish species showed several abnormal behaviors which included restlessness, arena movements, loss of equilibrium, increased opercular activities, strong spasm, paralysis and sudden quick movements during the exposure. For histopathological studies, A. testudineus, C. punctatus and B. gonionotus were exposed for 7 days to sublethal concentrations of 1.13 and 3.75 ppm; 1.13 and 2.26 ppm; and 1.13 and 2.26 ppm of Diazinon 60 EC, respectively. Hypertrophy, necrosis and pyknosis of hepatocytes, pyknosis and degenerative changes such as necrosis of tubular and haematopoietic cells of kidney were the major histopathological effects.

The distribution of phytoplankton pigments and the fishery of anchovy (Engraulis encrasicolus) in the Hellenic seas

A brief description of the Greek fisheries for the anchovy (Engraulis encrasicolus, Engraulidae) is given, with emphasis on the spatial distribution of the catch. Satellite images of phytoplankton pigment distribution obtained with NIMBUS-7 are used to explain local abundance of the dynamics of anchovy populations.

Size-composition of Annual Landings in the White Shrimp, Litopenaeus setiferus, Fishery of the Northern Gulf of Mexico, 1960–2006: Its Trend and Relationships with Other Fishery-dependent Variable

The potential for growth overfishing in the white shrimp, Litopenaeus setiferus, fishery of the northern Gulf of Mexico appears to have been of limited concern to Federal or state shrimp management entities, following the cataclysmic drop in white shrimp abundance in the 1940’s. As expected from surplus production theory, a decrease in size of shrimp in the annual landings accompanies increasing fishing effort, and can eventually reduce the value of the landings. Growth overfishing can exacerbate such decline in value of the annual landings. We characterize trends in size-composition of annual landings and other annual fishery-dependent variables in this fishery to determine relationships between selected pairs of these variables and to determine whether growth overfishing occurred during 1960–2006. Signs of growth overfishing were equivocal. For example, as nominal fishing effort increased, the initially upward, decelerating trend in annual yield approached a local maximum in the 1980’s. However, an accelerating upward trend in yield followed as effort continued to increase. Yield then reached its highest point in the time series in 2006, as nominal fishing effort declined due to exogenous factors outside the control of shrimp fishery managers. The quadratic relationship between annual yield and nominal fishing effort exhibited a local maximum of 5.24(107) pounds (≈ MSY) at a nominal fishing effort level of 1.38(105) days fished. However, annual yield showed a continuous increase with decrease in size of shrimp in the landings. Annual inflation-adjusted ex-vessel value of the landings peaked in 1989, preceded by a peak in annual inflation-adjusted ex-vessel value per pound (i.e. price) in 1983. Changes in size composition of shrimp landings and their economic effects should be included among guidelines for future management of this white shrimp

Precious Corals in Hawaii: Discovery of a New Bed and Revised Management Measures for Existing Beds

The fishery for deepwater precious corals in the Hawaiian Islands has experienced an on-and-off history for almost 40 years. In spite of this, research, driven primarily by the precious coral jewelry industry, remains active. In this paper, the results of deepwater surveys in 2000 and 2001 are reported. In summary, a new bed on the summit of Cross Seamount is described and revised estimates of MSY’s for pink coral, Corallium secundum; red coral, Corallium regale; and gold coral, Ger ardia sp., in the two known beds off Makapuu, Oahu, and Keahole Point, Hawaii, in the main Hawaiian Islands, are presented. The population dynamics of each species is described, as well as their ecological limits on Hawaii’s deep reefs, island shelves, and seamounts. The local supply of precious coral in the main Hawaiian Islands is sufficient to support the local industry, but cost/ benefits of selective harvest requirements and weather constraints limit profitability of the fish

Um esquema de Fourier local para análise tempo-frequência de sinais não-estacionários aplicado a ruído eletroquímico

Sinais diversos estão presentes em nosso cotidiano, assim como nas medidas realizadas nas atividades de ciência e tecnologia. Dentre estes sinais, tem grande importância tecnológica aqueles associados à corrosão de estruturas metálicas. Assim, esta tese propõe o estudo de um esquema local de transformada de Fourier janelada, com a janela variando em função da curtose, aplicada a sinais de ruído eletroquímico. A curtose foi avaliada nos domínios do tempo e da frequência e processada pelo programa desenvolvido para esse fim. O esquema foi aplicado a sinais de ruído eletroquímico dos aços UNS S31600, UNS G10200 e UNS S32750 imersos em três soluções: FeCl3 0,1 mol=L (cloreto férrico), H2SO4 5%(ácido sulfúrico) e NaOH 0,1%(hidróxido de sódio). Para os aços inoxidáveis, estas soluções promovem corrosão localizada, uniforme e passivação, respectivamente. Visando testar o desempenho do esquema de Fourier desenvolvido, testes foram realizados utilizando-se inicialmente sinais sintéticos e em seguida sinais de ruído eletroquímico. Notou-se que os sinais têm características de não-estacionaridade e a maior parte da energia está presente em baixa frequência. Os intervalos de tempo e de frequência onde se concentra a maior parte da energia do sinal foram correlacionados. Para os picos máximos dos sinais de potencial e corrente obtidos de amperimetria de resistência nula, a correlação entre eles foi baixa, independente da forma de corrosão presente. Conclui-se que o método se adaptou bastante bem às características locais do sinal eletroquímico permitindo o monitoramento dos espectros tempo-frequência. O fato de ser sensível às características locais do sinal permite analisar aspectos dos sinais que do modo clássico não podem ser diretamente processados. O método da transformada de Fourier janelada variável (Variable Short-Time Fourier Transform - VSTFT) adaptou-se muito bem no monitoramento dos sinais originados de potencial de circuito aberto e amperimetria de resistência nula.